Abstract

By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X,
such that the set of ℒ-regular countably additive bounded measures is sequentially closed in the set
of ℒ-regular finitely additive bounded measures on the algebra generated by ℒ
with the weak
topology.

For a pair of lattices ℒ1⊂ℒ2 in X sufficient conditions are indicated to determine when ℒ1
Alexandrov implies that ℒ2 is also Alexandrov and vice versa. The extension of this situation is
given where T:X→Y and ℒ1 and ℒ2 are lattices of subsets of X and Y respectively and T is ℒ1−ℒ2
continuous.

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